We develop techniques for obtaining the mirror of Calabi-Yau supermanifolds as super Landau-Ginzburg theories. In some cases the dual can be equivalent to a geometry. We apply this to some examples. In particular we show that the mirror of the twistorial Calabi-Yau CP 3|4 becomes equivalent to a quadric in CP 3|3 CP 3|3 as had been recently conjectured (in the limit where the Khler parameter of CP 3|4 , t ). Moreover we show using these techniques that there is a non-trivial Z 2 symmetry for the Khler parameter, t -t, which exchanges the opposite helicity states. As another class of examples, we show that the mirror of certain weighted projective (n + 1|1) superspaces is equivalent to compact Calabi-Yau hypersurfaces in weighted projective n space.
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Aganagic et al. (2004) studied this question.